"Mila Elle Smith graced the world with her arrival on Tuesday 4th December at 10:15pm. I have no words just an explosion of love that has filled my heart and the space around me," the caption read.
"Thank you to everyone for all the heart melting words and warm welcome we have received. Excuse me while I immerse in my family bubble."
Meanwhile, Dannii Minogue's ex recently gushed, "I could not love you any more even if I tried beautiful girl."
Smith confirmed on Instagram that he had become a dad for the second time.
On Wednesday evening he shared a touching Instagram post.
The dad penned, "Last night at 10.15pm the world became a better place, the birth of our baby girl Mila Elle has been the most magical adventure ever."
